Non-Nested Tests for Competing Models Estimated by Generalized Method of Moments

Abstract

Non-nested tests are proposed for competing models estimated by generalized method of moments. Results are presented for non-nested linear regression models with het- eroskedasticity and serial correlation of unknown form and differing instrument validity assumptions. Regression forms of the statistics are also presented. THIS PAPER IS CONCERNED with providing a procedure whereby non-nested models estimated by generalized method of moments (GMM) (Hansen (1982)) may be com- pared. In particular, Cox-type (Cox (1961, 1962)) and encompassing tests (Mizon and Richard (1986)) are proposed. Implicit in such tests is a degree of arbitrariness in the way the statistics are constructed as, typically, the assumptions underlying GMM estima- tion techniques are minimal and do not fully specify the data generation process (DGP) underlying the observable random variables, in contradistinction to the method of maximum likelihood. Our procedures allow the population moment conditions on which GMM estimation of the competing models is based to differ in the conditioning sets under which conditional expectation is taken; such differences may reflect different a priori assumptions concerning the exogeneity status of random variables in the models. These tests may be regarded as generalizations of Singleton (1985). More recent work includes Ghysels and Hall (1990) which requires the specification of the DGP under the null hypothesis and Wooldridge (1990b) which proposes heteroskedasticity-robust tests for non-nested non-linear regression models. Our results are specialized to provide non-nested tests for competing regression models estimated by instrumental variables, where we allow a degree of heteroskedastic- ity and serial correlation in the process generating the disturbance terms, by assuming appropriate mixing conditions (White (1984)), and the instrument validity assumptions to differ across the models; cf. Godfrey (1983, 1984) which assume a scalar covariance matrix for the disturbances and that the set of instruments is valid in both models. Thus, our framework includes models which may be both simultaneous and dynamic. Section 2 describes procedures for obtaining Cox-type and encompassing tests for competing models estimated by GMM. Section 3 specializes these results to competing linear regression models estimated by instrumental variables; regression forms for the statistics are presented. The paper is concluded by Section 4. In our presentation, we eschew detailed regularity assumptions.